xenharmonic (microtonal wiki) - 22edo tetrachords

A chart of all possible 22edo tetrachords (28 altogether):

Tetrachord details:

tetrachord notation	steps in cents	interval names	solfege	notes
1-1-7	55 + 55 + 382	P1 d2 m2 P4	do di ra fa
1-2-6	55 + 109 + 327	P1 d2 N2 P4	do di ru fa
1-3-5	55 + 164 + 273	P1 d2 M2 P4	do di re fa
1-4-4	55 + 218 + 218	P1 d2 sm3 P4	do di ma fa	found in Superpyth Phrygian
1-5-3	55 + 273 + 164	P1 d2 m3 P4	do di me fa
1-6-2	55 + 327 + 109	P1 d2 M3 P4	do di mi fa
1-7-1	55 + 382 + 55	P1 d2 SM3 P4	do di mo fa
2-1-6	109 + 55 + 327	P1 m2 N2 P4	do ra ru fa
2-2-5	109 + 109 + 273	P1 m2 M2 P4	do ra re fa
2-3-4	109 + 164 + 218	P1 m2 sm3 P4	do ra ma fa
2-4-3	109 + 218 +165	P1 m2 m3 P4	do ra me fa
2-5-2	109 + 273 + 109	P1 m2 M3 P4	do ra mi fa
2-6-1	109 + 327 + 55	P1 m2 SM3 P4	do ra mo fa
3-1-5	164 + 55 + 273	P1 N2 M2 P4	do ru re fa
3-2-4	164 + 109 + 218	P1 N2 sm3 P4	do ru ma fa
3-3-3	164 + 164 +164	P1 N2 m3 P4	do ru me fa	perfectly even tetrachord, found in Porcupine temperament
3-4-2	164 + 218 + 109	P1 N2 M3 P4	do ru mi fa
3-5-1	164 + 273 + 55	P1 N2 SM3 P4	do ru mo fa
4-1-4	218 + 55 + 218	P1 M2 sm3 P4	do re ma fa	found in Superpyth Minor (& Dorian)
4-2-3	218 + 109 + 164	P1 M2 m3 P4	do re me fa
4-3-2	218 + 164 + 109	P1 M2 M3 P4	do re mi fa
4-4-1	218 + 218 + 55	P1 M2 SM3 P4	do re mo fa	found in Superpyth Major (& Mixolydian, & Lydian)
5-1-3	273 + 55 + 164	P1 sm3 m3 P4	do ma me fa
5-2-2	273 + 109 + 109	P1 sm3 M3 P4	do ma mi fa
5-3-1	273 + 164 + 55	P1 sm3 SM3 P4	do ma mo fa
6-1-2	327 + 55 + 109	P1 m3 M3 P4	do me mi fa
6-2-1	327 + 109 + 55	P1 m3 SM3 P4	do me mo fa
7-1-1	382 + 55 + 55	P1 M3 SM3 P4	do mi mo fa

Tetrachords in families:

sML	MsL	sLM	MLs	LsM	LMs	genus	name(s) / notes
1-1-7		1-7-1		7-1-1		enharmonic	close to Didymos's Enharmonic, 32/31 • 31/30 • 5/4.
1-2-6	2-1-6	1-6-2	2-6-1	6-1-2	6-2-1	chromatic
1-3-5	3-1-5	1-5-3	3-5-1	5-1-3	5-3-1	chromatic
2-2-5		2-5-2		5-2-2		chromatic
2-3-4	3-2-4	2-4-3	3-4-2	4-2-3	4-3-2	diatonic	similar in function to JI tetrachord 16/15 • 9/8 • 10/9, but altered
1-1-4		1-4-1		4-1-1		diatonic	SuperPyth
3-3-3						diatonic	Porcupine